The precision required to characterize a Hamiltonian is central to developing advantageous quantum computers, providing powerful advances in quantum sensing and crosstalk mitigation. Traditional methods to determine a Hamiltonian are difficult due to the intricacies of quantum systems, involving numbers of equations and parameters that grow exponentially with the number of qubits. To mitigate these shortcomings, in this paper, we introduce an innovative and effective procedure integrating a physics-informed neural network (PINN) with a freezing mechanism to learn the Hamiltonian parameters efficiently. Although PINN and experimental data alone would become impractical as $N$ increases, the mechanism we introduce freezes the interactions of most of the qubits, leaving just a qubit subsystem to be analyzed by the PINN method. Determination of all physical parameters is accomplished by analyzing the system by parts until completion. We validated the efficacy of our method using simulation data obtained from the IBM quantum computer to obtain the training data and we found that a PINN can learn the two-qubit parameters with high accuracy, achieving a median error of less than $0.1%$ for systems of up to four qubits. We have successfully combined the PINN analysis of two qubits with the freezing mechanism in the case of a four-qubit system.
The precision required to characterize a Hamiltonian is central to developing advantageous quantum computers, providing powerful advances in quantum sensing and crosstalk mitigation. Traditional methods to determine a Hamiltonian are difficult due to the intricacies of quantum systems, involving numbers of equations and parameters that grow exponentially with the number of qubits. To mitigate these shortcomings, in this paper, we introduce an innovative and effective procedure integrating a physics-informed neural network (PINN) with a freezing mechanism to learn the Hamiltonian parameters efficiently. Although PINN and experimental data alone would become impractical as N increases, the mechanism we introduce freezes the interactions of most of the qubits, leaving just a qubit subsystem to be analyzed by the PINN method. Determination of all physical parameters is accomplished by analyzing the system by parts until completion. We validated the efficacy of our method using simulation data obtained from the IBM quantum computer to obtain the training data and we found that a PINN can learn the two-qubit parameters with high accuracy, achieving a median error of less than 0.1 for systems of up to four qubits. We have successfully combined the PINN analysis of two qubits with the freezing mechanism in the case of a four-qubit system.
Hamiltonian learning (HL), enabling precise estimation of system parameters and underlying dynamics, plays a critical role in characterizing quantum systems. However, conventional HL methods face challenges in noise robustness and resource efficiency, especially under limited measurements. In this work, we present Inverse Physics-Informed Neural Networks for Hamiltonian Learning (iPINN-HL), an approach that incorporates the Schrödinger equation as a soft constraint via a loss function penalty into the ML procedure. This formulation allows the model to integrate both observational data and known physical laws to infer Hamiltonian parameters with greater accuracy and resource efficiency. We benchmark iPINN-HL against a deep-neural-network-based quantum state tomography method [denoted as DNN-HL (Deep Neural Network for Hamiltonian Learning)] and demonstrate its effectiveness across several different scenarios, including one-dimensional spin chains, cross-resonance gate calibration, crosstalk identification, and real-time compensation to parameter drift. Our results show that iPINN-HL can approach the Heisenberg limit and exhibits robustness to noises, while outperforming DNN-HL in accuracy and resource efficiency. Therefore, iPINN-HL is a powerful and flexible framework for quantum system characterization for practical tasks.
This study introduces a quantum-accelerated framework that integrates quantum optimization with physics-informed neural networks (PINNs) to solve PDEs more efficiently. By leveraging the Quantum Approximate Optimization Algorithm (QAOA), the proposed framework enhances the initialization and boundary parameter optimization of PINNs, addressing key challenges such as slow convergence and high computational cost. The hybrid approach combines the data efficiency and physical constraint embedding capabilities of PINNs with the computational advantages of quantum optimization, enabling faster and more accurate solutions for complex PDEs. The framework was validated using the Shuhao Cao PDE dataset, demonstrating significant improvements in training efficiency and accuracy compared to traditional numerical solvers and classical PINNs. Experimental results highlight that quantum optimization effectively accelerates convergence by optimizing initial conditions and boundary constraints, reducing the computational overhead associated with classical training processes. Despite its reliance on emerging quantum hardware and the sensitivity of PINNs to hyperparameter selection, this approach offers a scalable and robust solution for solving high-dimensional PDEs. The findings underscore the potential of hybrid quantum-classical methods in advancing scientific computing, providing a foundation for future research in stochastic PDEs, multi-physics problems, and other real-world applications.
Quantum state tomography (QST) faces exponential measurement requirements and noise sensitivity in multi-qubit systems, bottlenecking practical quantum technologies. We present a physics-informed neural network (PINN) framework integrating quantum mechanical constraints via adaptive weighting, a residual-and-attention-enhanced architecture, and differentiable Cholesky parameterization for physical validity. Evaluations on 2--5 qubit systems and arbitrary-dimensional states show PINN consistently outperforms traditional neural networks (TNNs), achieving highest fidelity across all dimensions. PINN outperforms baselines, with marked improvements in moderately high-dimensional systems, superior noise robustness (slower performance degradation), and consistent dimensional robustness. Theoretical analysis shows physical constraints reduce Rademacher complexity and mitigate the curse of dimensionality via constraint-induced dimension and sample complexity reduction, effective regardless of qubit number. While experiments are limited to 5-qubit systems due to computational constraints, our theoretical framework (convergence guarantees, generalization bounds, scalability theorems) justifies PINN's advantages will persist and strengthen in larger systems (6+ qubits), where constraint-induced dimension reduction benefits grow with system size. Practically, this advances quantum error correction and gate calibration by reducing measurement requirements from O(4^n) to O(2^n) while maintaining high fidelity, enabling faster error correction cycles and accelerated calibration critical for scalable quantum computing.
Quantum Fisher Information (QFI) sets the ultimate precision limit for parameter estimation and is therefore a central quantity in quantum metrology. In time-dependent many-body systems, however, maximizing QFI is a highly non-trivial task due to the combined effects of non-commutativity, control complexity, and the exponential growth of the Hilbert space. In this work, we present a physics-informed neural network (PINN) framework to address this problem through the learning of counter-diabatic quantum dynamics. Our approach combines a variational PINN formulation with a Magnus-expansion treatment of time-ordered evolution, enabling the adiabatic gauge potential and the scheduling function to be inferred directly from the underlying physics while enforcing the Euler-Lagrange structure of the protocol. The method is applied to several families of driven spin Hamiltonians, including nearest-neighbor, dipolar, and trapped-ion-inspired interactions, for systems of up to six qubits. The numerical results show that the proposed framework systematically improves over reference solutions based only on the Euler-Lagrange condition, yielding high normalized QFI together with favorable fidelity and extremal-balance metrics while preserving small phsical residuals. The analysis further shows that learning the scheduling function provides a clear performance advantage in most cases, and reveals non-trivial finite-size effects, with q=3 emerging as a particularly challenging regime. Although scalability remains limited by the exponential growth of the operator space and by automatic-differentiation costs, the results demonstrate that PINNs constitute a viable and physically grounded route for learning metrologically optimal control strategies in interacting quantum systems.
Physics-Informed Neural Networks (PINN) emerged as a powerful tool for solving scientific computing problems, ranging from the solution of Partial Differential Equations to data assimilation tasks. One of the advantages of using PINN is to leverage the usage of Machine Learning computational frameworks relying on the combined usage of CPUs and co-processors, such as accelerators, to achieve maximum performance. This work investigates the design, implementation, and performance of PINNs, using the Quantum Processing Unit (QPU) co-processor. We design a simple Quantum PINN to solve the one-dimensional Poisson problem using a Continuous Variable (CV) quantum computing framework. We discuss the impact of different optimizers, PINN residual formulation, and quantum neural network depth on the quantum PINN accuracy. We show that the optimizer exploration of the training landscape in the case of quantum PINN is not as effective as in classical PINN, and basic Stochastic Gradient Descent (SGD) optimizers outperform adaptive and high-order optimizers. Finally, we highlight the difference in methods and algorithms between quantum and classical PINNs and outline future research challenges for quantum PINN development.
Recently, a novel type of Neural Network (NNs): the Physics-Informed Neural Networks (PINNs), was discovered to have many applications in computational physics. By integrating knowledge of physical laws and processes in Partial Differential Equations (PDEs), fast convergence and effective solutions are obtained. Since training modern Machine Learning (ML) systems is a computationally intensive endeavour, using Quantum Computing (QC) in the ML pipeline attracts increasing interest. Indeed, since several Quantum Machine Learning (QML) algorithms have already been implemented on present-day noisy intermediate-scale quantum devices, experts expect that ML on reliable, large-scale quantum computers will soon become a reality. However, after potential benefits from quantum speedup, QML may also entail reliability, trustworthiness, safety, and security risks. To solve the challenges of QML, we combine classical information processing, quantum manipulation, and processing with PINNs to accomplish a hybrid QML model named quantum based PINNs.